Heavy quark potential in the quark-gluon plasma: Deep neural network meets lattice quantum chromodynamics
Shuzhe Shi, Kai Zhou, Jiaxing Zhao, Swagato Mukherjee, Pengfei Zhuang
Abstract
Bottomonium states are key probes for experimental studies of the quark-gluon plasma (QGP) created in high-energy nuclear collisions. Theoretical models of bottomonium productions in high-energy nuclear collisions rely on the in-medium interactions between the bottom and antibottom quarks. The latter can be characterized by the temperature ($T$) dependent potential, with real (${V}_{R}(T,r)$) and imaginary (${V}_{I}(T,r)$) parts, as a function of the spatial separation ($r$). Recently, the masses and thermal widths of up to $3S$ and $2P$ bottomonium states in QGP were calculated using lattice quantum chromodynamics (LQCD). Starting from these LQCD results and through a novel application of deep neural network, here, we obtain ${V}_{R}(T,r)$ and ${V}_{I}(T,r)$ in a model-independent fashion. The temperature dependence of ${V}_{R}(T,r)$ was found to be very mild between $T\ensuremath{\approx}0--334\text{ }\text{ }\mathrm{MeV}$. For $T=151--334\text{ }\text{ }\mathrm{MeV}$, ${V}_{I}(T,r)$ shows a rapid increase with $T$ and $r$, which is much larger than the perturbation-theory-based expectations.